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Dynamics and Control of Biological Systems
Chapter 24 addresses a variety of analysis problems in the field of biosystems:
• Systems Biology• Gene Regulation
• Circadian Rhythm Clock Network• Signal Transduction Networks
• Chemotaxis• Insulin Mediated Glucose Uptake• Simple Phosphorylation Transduction Cascade
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What is “Systems Biology”?[WTEC Benchmark Study (2005): M. Cassman, A. Arkin, F. Doyle, F. Katagiri, D. Lauffenburger, C. Stokes]
[also: Nature, Dec 22, 2005]
Primary Definition: The understanding of biological network behavior through the application of modeling and simulation, tightly linked to experiment
Related Ideas– Identification and validation of networks– Creation of appropriate datasets– Development of tools for data acquisition and software
Motivation: Phenotype is governed by the behavior of networks, rather than the operation of single genes. Understanding the dynamics of even the simplest biological networks requires the application of modeling and simulation.
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Folding Process
Synthesis of Heat Shock Proteins
(FtsH and DnaK)
DNAKBinding to s32
s32
SynthesisHEAT
Folded Proteins32++
Figure 24.1 Feedback and feedforward control loops that regulate heat shock in bacteria (modified from El-Samad, et
al., 2006).
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Transcription
LIGHT
PERTranslation
Phosphorylation & Dimerization of PER, CRY
cryTranscription
CRYTranslation
Nucleus
CytoplasmCell Membrane
Figure 24.2 The gene regulatory circuit responsible for mammalian circadian rhythms.
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Transcription
Nucleus
Cytoplasm
Cell Membrane
Nuclear Transport
Translation ProteinActivation
primarytranscript mRNA protein
activeprotein
Figure 24.3 The layers of feedback control in the Central Dogma (modified from (Alberts et al., 1998))
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G1
Autoregulation
TF1
Multi-Component Loop
G1
TF1
TF2
G2G1TF1
FeedforwardLoop
TF2
G2
G1
SIMO Module
TF1
MIMO Module
G1TF1
Regulator Chain
TF2 G2 TF3 G3
G2 G3 G1 G2 G3
TF1 TF2
Figure 24.4 Examples of circuit motifs in yeast (adapted from (Lee et al., 2002)). The rectangles denote promoter regions on a
gene (G1, G2, etc.) and the circles are transcription factors (TF1, TF2, etc.).
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Process Control Concept Biological Control Analog
Sensor Concentration of a protein
Setpoint Implicit: equilibrium concentration of protein
Controller Transcription factors
Final control element Transcription apparatus; ribosomal
machinery for protein translation
Process Cellular homeostasis
Table 24.1 Analogies between process control concepts and gene transcription control concepts.
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Circadian Rhythms
Circadian rhythms = self-sustained biological rhythms characterized by a free-running period of about 24h (circa diem)
Circadian rhythms characteristics:• General – bacteria, fungi, plants, flies, fish, mice, humans, etc.• Entrainment by light-dark cycles (zeitgeber)• Phase shifting by light pulses• Temperature compensation
Circadian rhythms occur at the molecular level
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Drosophila Circadian Oscillator
PER
TIM
PERTIM
PERTIM
DBT
PERP
P
TIMP
P
DBT
Cytoplasm
Nucleus
pertim
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perTranscription
LIGHT
PERTranslation
Phosphorylation & Dimerization of PER, TIM
timTranscription
TIMTranslation
Nucleus
CytoplasmCell Membrane
TIMDegradation
TranscriptionProcess
LIGHT
Protein (P)Translation and
DegradationProcesses
mRNA(M)
Figure 24.5 Schematic of negative feedback control of Drosophila circadian clock (adapted from (Tyson et al., 1999)):
detailed system (top), and simplified model (bottom).
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0 20 40 60 80 1000
1
2
3
mR
NA
Time (h)
0 20 40 60 80 1000
1
2
3
4
Pro
tein
Time (h)
Figure 24.6 Simulation of the circadian clock model.
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0 20 40 60 80 1000
1
2
3
4
mR
NA
Time (h)
0 20 40 60 80 1000
2
4
6P
rote
in
Time (h)
Figure 24.7 Simulation of circadian clock model for varying values of m (1.0 (solid), 1.1 (dashed), 1.5 (dash-dot), 2.0
(dotted), 4.0 (asterisk)).
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0 50 100 150 200 250 300 350 4000
2
4
mR
NA
Time (h)
0 50 100 150 200 250 300 350 4000
5
Pro
tein
Time (h)
0 50 100 150 200 250 300 350 400
100
200
Ke
q
Time (h)
Figure 24.8 Simulation of circadian clock model for entraining signal with period of 20 h.
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Implications from Systems Biology Studies
• Robustness characteristics of feedback architecture under stochastic uncertainty
• Underlying design principles
• Nature of entrainment, and systems characterization
• Possible therapeutic ramifications (mutants, etc.)
• General biological oscillator insights
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Bacterial Chemotaxis
Process by which motile bacteria sense chemical gradients and move in favorable directions
E. coli alternates between:– Smooth runs (flagella spin counterclockwise)
– Tumble (flagella spin clockwise)
Random walk that is biased towards chemical gradient
Impossible to detect gradient across length of body
Key property: perfect adaptation– Steady-state tumbling frequency in uniform environment is independent of
environment concentration level
[wikipedia]
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Cell Membrane
LIGAND
Motor(tumble)
Yphosphorylation
Ydephosphorylation
CheW-CheAmethylation
CheW-CheAdemethylationCheR
CheZ
CheYp
CheY
Bphosphorylation
Bdephosphorylation
CheBp
CheB
Figure 24.9 Schematic of chemotaxis signaling pathway in E. coli (adapted from Rao et al., 2004).
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Ky
-x
y0
u ++++
-1s
Figure 24.10 Integral control feedback circuit representation of chemotaxis (adapted from Yi et al., 2000).
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Insights Gained from Systems Biology Approach
• Study reveals that robustness facilitates analysis (specific parameters not required, module can be isolated)
• Robustness properties point to reliable performance over environmental perturbations or mutations – suggesting preference for evolution
• Rao et al. study points to limitations in homologous gene analysis
• Narrowly tuned ranges are often key for homeostasis, and integral control can help attain such performance
• Integral control leads to robustness in biochemical networks
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Type 2 Diabetes Mellitus
A metabolic disorder primarily characterized by hyperglycemia and insulin resistance
US: 14 million with associated annual medical costs of $132 billion
Worldwide: 350 million by the year 2030
Linked to obesity due to high caloric intake combined with low physical activity – progresses through insulin resistance
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Cell Membrane
INSULIN
Insulin ReceptorDynamics
CheZ
RECEPTOR
Signal Transduction
Cascade
GlucoseTransporter
Biomechanics
GLUT4
Figure 24.11 Simplified insulin signaling pathway for glucose uptake.